Wavelet spectral finite element for wave propagation in shear deformable laminated composite plates

Abstract

This paper presents a new 2-D wavelet spectral finite element (WSFE) model for studying wave propagation in thin to moderately thick anisotropic composite laminates. The WSFE formulation is based on the first order shear deformation theory (FSDT) which yields accurate results for wave motion at high frequencies. The wave equations are reduced to ordinary differential equations (ODEs) using Daubechies compactly supported, orthonormal, scaling functions for approximations in time and one spatial dimension. The ODEs are decoupled through an eigenvalue analysis and then solved exactly to obtain the shape functions used in element formulation. The developed spectral element captures the exact inertial distribution, hence a single element is sufficient to model a laminate of any dimension in the absence of discontinuities. The 2-D WSFE model is highly efficient computationally and provides a direct relationship between system input and output in the frequency domain. Results for axial and transverse wave propagations in laminated composite plates of various configurations show excellent agreement with finite element simulations using Abaqus®.